Demultiplexing filter and method

1. A demultiplexed filtering method, comprising: propagating an optical beam from an input optical fiber through a lens to a diffraction grating to produce: (i) a first diffracted beam, a center-wavelength thereof equaling a first center-wavelength of a first channel of the optical beam, that propagates back toward the input optical fiber at a first diffracted angle determined in part by the first center-wavelength and a diffraction order m1 of the first diffracted beam; and (ii) a second diffracted beam, a center-wavelength thereof equaling a second center-wavelength of a second channel of the optical beam and exceeding the first center wavelength, that propagates back toward the input optical fiber at a second diffracted angle determined in part by the second center-wavelength and a diffraction order m2 of the second diffracted beam that is less than the diffraction order m1; wherein the lens has a ray propagated therethrough without refraction, such that a propagation angle of the ray is the same on each side of lens; coupling the first diffracted beam into a first optical fiber of a one-dimensional optical-fiber array that includes the input optical fiber; and coupling the second diffracted beam into a second optical fiber of the one-dimensional optical-fiber array.

2. The method of claim 1, further comprising: collimating the optical beam with the lens located between a tip of the input optical fiber and the diffraction grating; and said coupling comprising focusing first diffracted beam and the second diffracted beam with the lens.

3. The method of claim 1, further comprising coupling the third diffracted beam into a third optical fiber of the one-dimensional optical-fiber array, wherein said propagating the optical beam to the grating also produces the third diffracted beam, a center wavelength thereof equaling the third center wavelength of a third channel of the optical beam and exceeding the second center wavelength, that propagates back toward the input optical fiber at a third diffracted angle determined in part by the third center-wavelength and a diffraction order m3 of the third diffracted beam that is less than the diffraction order m2.

4. The method of claim 1, further comprising collimating the optical beam with the lens located between a tip of the input optical fiber and the diffraction grating; a distance between the first optical fiber and an optical axis of the lens being equal to feff·tan(βout1−θaxis); where feff is an effective focal length of the lens, βout1 is an angle between the first diffracted beam and a surface-normal of the diffraction grating, and θaxis is an angle between the surface-normal and the optical axis in a plane that includes the one-dimensional optical-fiber array, and βout1=arcsin(m1λ1/Λ−sin [θaxis+arctan(ymp/feff)]), where λ1 is the first center wavelength, Λ is a period of the diffraction grating, and ymp is the distance between the input optical fiber and the optical axis; and a distance between the second optical fiber and an optical axis of the lens being equal to feff·tan(βout2−θaxis); βout2 is an angle between the first diffracted beam and a surface-normal of the diffraction grating, and βout2=arcsin(m2λ2/Λ−sin [θaxis+arctan(ymp/feff)]), where λ2 is the second center-wavelength.

5. The method of claim 4, diffraction order m2 being greater than one.

6. The method of claim 1, further comprising: propagating a multiplexed probe beam through a combustion zone, the optical beam being the multiplexed probe beam after transmission through the combustion zone; and coupling the optical beam into the input optical fiber.

7. A demultiplexing filter, comprising: an optical-fiber array comprising an input optical fiber having a fiber optical axis and an input fiber end-face, a surface thereof defining a fiber end-face plane; a first output optical fiber having a first fiber end-face that is substantially coplanar to the fiber end-face plane, and a first optical axis that is parallel to and coplanar with the fiber optical axis; and a second output optical fiber having a second fiber end-face that is coplanar to the fiber end-face plane to within a predetermined tolerance, and a second optical axis that is parallel to and coplanar with the fiber optical axis, the input fiber end-face, the first fiber end-face, and the second fiber end-face being collinear; a diffraction grating having a blazed diffractive surface facing the fiber end-face plane and tilted, with respect to the fiber optical axis, by a tilt angle that deviates from a blaze angle of the blazed diffractive surface by between 0.05 and 0.5 degrees; and a lens along an optical path between the optical-fiber array and the diffraction grating, having a lens optical-axis perpendicular to the fiber end-face plane and configured to propagate a ray therethrough without refraction, such that a propagation angle of the ray is the same on each side of lens, and the lens further configured to form an image of the blazed diffractive surface in a focal plane that is substantially coplanar with the fiber end-face plane.

8. The demultiplexing filter of claim 7, a distance between the fiber end-face plane and a principal plane of the lens being substantially equal to an effective focal length of the lens.

9. The demultiplexing filter of claim 7, at least one of the input optical fiber, the first output optical fiber and the second output optical fiber operating as a multi-mode fiber in a wavelength range between 1.3 micrometers and 2.5 micrometers.

10. The demultiplexing filter of claim 7, at least one of the input optical fiber, the first output optical fiber, and the second output optical fiber having a fiber core diameter than exceeds fifty micrometers.

11. The demultiplexing filter of claim 7, wherein: the input optical fiber emits an optical beam including a first optical channel having a first center-wavelength and a second optical channel having a second center-wavelength exceeding the first center-wavelength; the lens collimates the optical beam; and the diffraction grating generates, from the collimated optical beam, (i) a first diffracted beam, a center-wavelength thereof equal to the first center-wavelength, that propagates back toward the optical-fiber array at a first diffracted angle between the first diffracted beam and a surface-normal of the diffraction grating determined by the first center-wavelength and a diffraction order m1 of the first diffracted beam, and (ii) a second diffracted beam, a center-wavelength thereof equal to the second center-wavelength, that propagates back toward the optical-fiber array at a second diffracted angle between the second diffracted beam and the surface-normal determined by the second center-wavelength and a diffraction order m2 of the second diffracted beam that is less than the diffraction order m1.

12. The demultiplexing filter of claim 11, each of the first center-wavelength and the second center-wavelength being between 1.3 micrometers and 2.5 micrometers.

13. The demultiplexing filter of claim 11, at least one of the first center-wavelength and the second center-wavelength corresponding to an absorption line of one of carbon monoxide, water, and carbon dioxide.

14. The demultiplexing filter of claim 11, the input optical fiber having a core radius a0 and a numerical aperture NA0 such that a parameter 2π(a0/λ2)NA0 is greater than or equal to 2.405 to ensure multi-mode operation at both the first center-wavelength and the second center-wavelength, denoted by λ2; the first output optical fiber having a core radius a1 and a numerical aperture NA1 such that a parameter 2π(a1/λ1)NA1 is greater than or equal to 2.405 to ensure multi-mode operation at the first center-wavelength, denoted by λ1; the second optical fiber having a core radius a2 and a numerical aperture NA2 such that a parameter 2π(a2/λ2)NA2 is greater than or equal to 2.405 to ensure multi-mode operation at the second center-wavelength.

15. The demultiplexing filter of claim 11, diffraction order m2 being greater than one.

16. The demultiplexing filter of claim 11, the diffraction grating having a grating period greater than four times the second center-wavelength.

17. The demultiplexing filter of claim 11, further comprising a plurality of lasers optically coupled to the input optical fiber, to generate the optical beam.

18. The demultiplexing filter of claim 11, the emitted optical beam including a third optical channel having a third center-wavelength that exceeds the second center-wavelength; the optical-fiber array including a third output optical fiber having a third fiber end-face that is coplanar to the fiber end-face plane to within the predetermined tolerance and collinear with the first and second fiber end-faces, and a third optical axis that is parallel to and coplanar with an input-fiber optical axis; and wherein the diffraction grating generates, from the collimated optical beam, a third diffracted beam, a center-wavelength thereof equal to the third center-wavelength, that propagates back toward the optical-fiber array at a third diffracted angle determined in part by the third center-wavelength and a diffraction order m3 of the third diffracted beam that is less than the diffraction order m2.

19. The demultiplexing filter of claim 11, the diffraction grating having a period Λ, an ideal grating blaze-angle for Littrow-configuration operation at the first center-wavelength and the second center-wavelength being ϕ1=arctan (m1λ1/(2Λ)) and ϕ2=arctan (m2λ2/(2Λ)) respectively, where λ1 and λ2 denote the first and second center wavelengths respectively, the diffraction grating having a grating blaze-angle θB that differs from each of grating blaze-angles ϕ1 and ϕ2 by less than five degrees.

20. The demultiplexing filter of claim 11, a distance between the first output optical fiber and the lens optical-axis being equal to feff·tan (βout1−θaxis); where feff is an effective focal length of the lens, where βout1 is the first diffraction angle, and θaxis is an angle between the surface-normal and the lens optical-axis in a plane that includes the optical-fiber array; and a distance between the second output optical fiber and the lens optical-axis of the lens being equal to feff·tan(βout2−θaxis), where βout2 is the second diffraction angle.

21. The demultiplexing filter of claim 20, the first diffracted angle βout1 equaling arcsin (m1λ1/Λ−sin [θaxis+arctan(ymp/feff)]), where λ1 is the first center wavelength, Λ is a period of the diffraction grating, and ymp is the distance between the input optical fiber and the lens optical axis; and the second diffracted angle βout2 equaling arcsin(m212/Λ−sin [θaxis+arctan(ymp/feff)]), where λ2 is the second center-wavelength.

22. The demultiplexing filter of claim 20, the emitted optical beam including a third optical channel having a third center-wavelength that exceeds the second center-wavelength; the optical-fiber array including a third output optical fiber having a third fiber end-face that is coplanar to the fiber end-face plane to within the predetermined tolerance and collinear with the first and second fiber end-faces, and a third optical axis that is parallel to and coplanar with an input-fiber optical axis; the diffraction grating configured to generate, from the collimated optical beam, a third diffracted beam, a center-wavelength thereof equal to the third center-wavelength, that propagates back toward the optical-fiber array at a third diffracted angle determined in part by the third center-wavelength and a diffraction order m3 of the third diffracted beam that is less than the diffraction order m2; and a distance between the third output optical fiber and the lens optical-axis of the lens being equal to feff·tan(βout3−θaxis), where βout3 is the third diffraction angle.

23. The demultiplexing filter of claim 22, the third diffraction angle βout3 equaling arcsin(m3λ3/Λ−sin [θaxis+arctan(ymp/feff)]), where λ3 is the third center-wavelength.

24. A method for measuring species concentration in a combustion zone, comprising: propagating a multiplexed input probe beam through a lens in the combustion zone to produce an output probe beam, the combustion zone including (i) a first gas-phase species that has an absorption line at a first center-wavelength and (ii) a second gas-phase species that has an absorption line at a second center wavelength that exceeds the first center-wavelength, the lens having a ray propagated therethrough without refraction, such that a propagation angle of the ray is the same on each side of lens; coupling the output probe beam into an input optical fiber; propagating the output probe beam from the input optical fiber to a diffraction grating to produce; (i) a first diffracted beam, a center-wavelength thereof equaling the first center-wavelength, that propagates back toward the input optical fiber at a first diffracted angle determined in part by the first center-wavelength and a diffraction order m1 of the first diffracted beam; and (ii) a second diffracted beam, a center-wavelength thereof equaling the second center-wavelength, that propagates back toward the input optical fiber at a second diffracted angle determined in part by the second center-wavelength and a diffraction order m2 of the second diffracted beam that is less than the diffraction order m1; coupling the first diffracted beam into a first optical fiber of a one-dimensional optical-fiber array that includes the input optical fiber; coupling the second diffracted beam into a second optical fiber of the one-dimensional optical-fiber array; measuring (i) a first signal amplitude of the first diffracted beam output from the first optical fiber and (ii) a second signal amplitude of the second diffracted beam output from the second optical fiber; determining (i) from the first signal amplitude, a concentration of the first gas-phase species and the second gas-phase species.